It's undeniable that the Galaxy Note 10 and 10+ are the "best" stylus phones you can buy, but they're incredibly expensive. If you want a stylus that lives in your phone and don't feel like spending $1,000 to get it, the LG Stylo 5 might do the trick. This phone is easier to get now that it's available unlocked in the US, priced at $299.99.
The LG Stylo 5 is a modestly specced device with a Snapdragon 450 and 3GB of RAM. The 6.2-inch 1080p LCD gets the job done, and there's a capacitive stylus that docks inside the phone. There's a fingerprint sensor around back, along with a single 13MP camera.
Not only is this phone unlocked, but it also works on all major US carriers (CDMA and GSM). The phone costs $299.99, which is a bit more than carriers were asking at launch. However, Best Buy will knock $50 off the price if you activate on Verizon or AT&T and $100 off if you activate on Sprint. There's also a slightly cheaper Amazon version with bundled Amazon apps.